Maybe you didn’t duplicate the project in the process?
I just did this and it works as I indicated. But it’s a few steps and there’s some cleanup.
You’re multihoming the tasks to be copied into a new, temporary project in order to allow you to use Duplicate on that new project. After that, multiselect the newly created tasks in the newly created project and change their project membership to the original project, specifying the section to be “copied” to. Now your tasks are “moved.” You’ll then have to delete the new temporary project.
Larry